Optical scanning apparatus, multi-beam optical scanning apparatus, and image-forming apparatus

ABSTRACT

Provided are compact, high-definition, optical scanning apparatus and multi-beam scanning apparatus capable of keeping the spot size uniform in the sub-scanning direction throughout the entire, effective scanning area on a surface to be scanned. An optical scanning apparatus has an entrance optical system  11  for guiding light emitted from a light source  1 , to a deflector  5 , and a scanning optical system  6  for focusing the light reflectively deflected by the deflector, on a surface to be scanned  7 . In the optical scanning apparatus, the scanning optical system has a plurality of sagittal asymmetric change surfaces in which curvatures in the sagittal direction change on an asymmetric basis in the meridional direction with respect to the optical axis of the scanning optical system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to optical scanning apparatus andmulti-beam optical scanning apparatus and, particularly, the inventionis suitably applicable to image-forming apparatus, for example, such aslaser beam printers involving the electrophotographic process, digitalcopiers, and the like, constructed so as to record image information byreflectively deflecting light from light source means by deflectingmeans to optically scan a surface to be scanned, via scanning opticalmeans with the light.

2. Related Background Art

In the optical scanning apparatus such as the laser beam printers, thedigital copiers, etc. heretofore, the image information was recorded insuch a manner that the light optically modulated according to an imagesignal and outputted from the light source means was periodicallydeflected by the deflecting means which consisted of, for example, apolygon mirror, and was converged in a spot shape on a surface of aphotosensitive recording medium by the scanning optical means with thefθ characteristics to optically scan the surface.

FIG. 13 is a schematic diagram to show the principal part of aconventional, optical scanning apparatus. In the same figure a divergingbeam emitted from the light source means 91 is converted into a nearlyparallel beam by a collimator lens 92 and the nearly parallel beam isrestricted in the beam width by a stop 93 to enter a cylindrical lens 94having a predetermined power only in the sub-scanning direction. Thenearly parallel beam entering the cylindrical lens 94 emerges in thestate of the nearly parallel beam in the main scanning section as it is.In the sub-scanning section the beam is converged to be focused into analmost linear image on a deflection facet (reflective surface) 95 a ofan optical deflector 95 consisting of a polygon mirror. Then thescanning optical means (fθ lens system) 96 with the fθ characteristicsguides the beam reflectively deflected by the deflection facet 95 a ofthe optical deflector 95, via a return mirror 98 to a surface ofphotosensitive drum 97 as a surface to be scanned. The optical deflector95 is rotated at nearly equal angular velocity, whereby the beam scansthe surface to be scanned 97 at almost constant speed to record theimage information thereon.

To make the apparatus from the optical deflector 95 to the surface to bescanned 97 more compact, it is necessary to effect good correction foroptical performance of the fθ lens 96 throughout wide angles of view.For example, Japanese Patent Application Laid-Open No. 7-113950discloses an example of correction for curvature of field (imagepositions) in the sub-scanning direction and at wide angles of view byprovision of only one surface wherein curvatures in the sagittaldirection vary on an asymmetric basis with respect to the optical axisand wherein magnitude relations of curvatures in the sagittal directionare different on the upper and lower sides of the optical axis.

There was, however, the problem that nonuniformity of lateralmagnification (which will also be referred to hereinafter as“sub-scanning magnification”) in the sub-scanning direction appearedprominent at wide angles of view and even if the image positions in thesub-scanning direction were corrected the spot size would vary inproportion to sub-scanning magnifications at respective scanningpositions. Further, in the case of the optical scanning apparatus usingmultiple beams, they suffered from the problem that with deviation ofthe sub-scanning magnifications from a fixed value, line pitch intervalsin the sub-scanning direction varied at every scanning position on thesurface to be scanned during the optical scanning of that surface, so asto result in irregular pitch.

The scanning optical means needs to be located near the opticaldeflector in order to decrease the cost by decreasing the size of thelens. However, there was the problem that it increased the sub-scanningmagnification and the asymmetry of the image positions in thesub-scanning direction and the asymmetry of the sub-scanningmagnifications appeared more prominent.

An object of the present invention is to provide a compact,high-definition, optical scanning apparatus with wide angles of viewcapable of effecting good correction for curvature of field (imagepositions) in the sub-scanning direction and correction to keep thesub-scanning magnification at a fixed value, by constructing thescanning optical means of a plurality of sagittal asymmetric changesurfaces and properly setting the shape of each lens.

Another object of the present invention is to provide a compact,high-definition, multi-beam optical scanning apparatus with wide anglesof view capable of keeping line pitch intervals in the sub-scanningdirection constant throughout the entire, effective scanning area, byconstructing the scanning optical means of a plurality of sagittalasymmetric change surfaces and properly setting the shape of each lens.

SUMMARY OF THE INVENTION

A scanning optical apparatus according to one aspect of the invention isan optical scanning apparatus comprising entrance optical means forguiding light emitted from light source means, to deflecting means, andscanning optical means for focusing the light reflectively deflected bythe deflecting means, on a surface to be scanned,

-   -   wherein the scanning optical means comprises a plurality of        sagittal asymmetric change surfaces in which curvatures in the        sagittal direction change on an asymmetric basis in the        meridional direction with respect to the optical axis of the        scanning optical means.

In the optical scanning apparatus according to another aspect of theinvention, said sagittal asymmetric change surfaces comprise two or moresagittal modification surfaces in which magnitude relation differs amongcurvatures in the sagittal direction at respective positions in themeridional direction with respect to the optical axis.

In the optical scanning apparatus according to another aspect of theinvention, said sagittal deformation surfaces comprise two or moresurfaces in which the curvatures in the sagittal direction at therespective positions in the meridional direction with respect to theoptical axis become large or small on the same side.

In the optical scanning apparatus according to another aspect of theinvention, in at least one surface of said sagittal deformation surfacesthe curvatures in the sagittal direction become large on the side ofsaid light source means with respect to the optical axis.

In the optical scanning apparatus according to another aspect of theinvention, in at least one surface of said sagittal asymmetric changesurfaces the curvatures in the sagittal direction have an inflectionpoint only on one side in the meridional direction with respect to theoptical axis.

In the optical scanning apparatus according to another aspect of theinvention, said scanning optical means comprises a plurality of fθlenses, an fθ lens located closest to the deflecting means out of saidplurality of fθ lenses has a negative, refractive power in thesub-scanning direction, and an fθ lens located closest to the surface tobe scanned has a positive, refractive power in the sub-scanningdirection.

In the optical scanning apparatus according to another aspect of theinvention, all lens surfaces of said plurality of fθ lenses are formedin a concave shape opposed to said deflecting means.

In the optical scanning apparatus according to another aspect of theinvention, the following condition is satisfied:k/W≦0.6

-   -   where k is an fθ coefficient of said scanning optical means and        W an effective scanning width on said surface to be scanned.

In the optical scanning apparatus according to another aspect of theinvention, the following condition is satisfied:|β_(s)|≧2

-   -   where β_(s) is a lateral magnification in the sub-scanning        direction of said scanning optical means.

A multi-beam optical scanning apparatus according to a further aspect ofthe invention is a multi-beam optical scanning apparatus comprisinglight source means having a plurality of light-emitting regions,entrance optical means for guiding a plurality of beams emitted from thelight source means, to deflecting means, and scanning optical means forfocusing the plurality of beams reflectively deflected by the deflectingmeans, on a surface to be scanned,

-   -   wherein said scanning optical means comprises a plurality of        sagittal asymmetric change surfaces in which curvatures in the        sagittal direction change on an asymmetric basis in the        meridional direction with respect to the optical axis of the        scanning optical means.

In the multi-beam optical scanning apparatus according to another aspectof the invention, said sagittal asymmetric change surfaces comprise twoor more sagittal modification surfaces in which magnitude relationdiffers among curvatures in the sagittal direction at respectivepositions in the meridional direction with respect to the optical axis.

In the multi-beam optical scanning apparatus according to another aspectof the invention, said sagittal deformation surfaces comprise two ormore surfaces in which the curvatures in the sagittal direction at therespective positions in the meridional direction with respect to theoptical axis become large or small on the same side.

In the multi-beam optical scanning apparatus according to another aspectof the invention, in at least one surface of said sagittal deformationsurfaces the curvatures in the sagittal direction become large on theside of said light source means with respect to the optical axis.

In the multi-beam optical scanning apparatus according to another aspectof the invention, in at least one surface of said sagittal asymmetricchange surfaces the curvatures in the sagittal direction have aninflection point only on one side in the meridional direction withrespect to the optical axis.

In the multi-beam optical scanning apparatus according to another aspectof the invention, said scanning optical means comprises a plurality offθ lenses, an fθ lens located closest to the deflecting means out ofsaid plurality of fθ lenses has a negative, refractive power in thesub-scanning direction, and an fθ lens located closest to the surface tobe scanned has a positive, refractive power in the sub-scanningdirection.

In the multi-beam optical scanning apparatus according to another aspectof the invention, all lens surfaces of said plurality of fθ lenses areformed in a concave shape opposed to said deflecting means.

In the multi-beam optical scanning apparatus according to another aspectof the invention, the following condition is satisfied:k/W≦0.6

-   -   where k is an fθ coefficient of said scanning optical means and        W an effective scanning width on said surface to be scanned.

In the multi-beam optical scanning apparatus according to another aspectof the invention, the following condition is satisfied:|β_(s)|≧2

-   -   where β_(s) is a lateral magnification in the sub-scanning        direction of said scanning optical means.

An image-forming apparatus according to a further aspect of theinvention is an image-forming apparatus comprising the scanning opticalapparatus as set forth, a photosensitive body located at said surface tobe scanned, a developing unit for developing an electrostatic, latentimage formed on said photosensitive body with the light under scan bysaid scanning optical apparatus, into a toner image, a transfer unit fortransferring said developed toner image onto a transfer medium, and afixing unit for fixing the transferred toner image on the transfermedium.

Another image-forming apparatus according to a further aspect of thepresent invention is an image-forming apparatus comprising the scanningoptical apparatus as set forth, and a printer controller for convertingcode data supplied from an external device, into an image signal andsupplying the image signal to said scanning optical apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view along the main scanning direction ofthe optical scanning apparatus in Embodiment 1 of the present invention;

FIG. 2 is a cross-sectional view along the sub-scanning direction of theoptical scanning apparatus in Embodiment 1 of the present invention;

FIG. 3 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 1 of the present invention;

FIG. 4 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 1 of the present invention;

FIG. 5 is an aberration diagram of the scanning optical means inEmbodiment 1 of the present invention;

FIG. 6 is an aberration diagram of the scanning optical means inEmbodiment 1 of the present invention, and a comparative example;

FIG. 7 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 2 of the present invention;

FIG. 8 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 2 of the present invention;

FIG. 9 is an aberration diagram of the scanning optical means inEmbodiment 2 of the present invention;

FIG. 10 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 3 of the present invention;

FIG. 11 is a diagram to show change in curvatures in the sagittaldirection in each of surfaces of the scanning optical means inEmbodiment 3 of the present invention;

FIG. 12 is an aberration diagram of the scanning optical means inEmbodiment 3 of the present invention;

FIG. 13 is a schematic diagram of principal part to show a conventional,optical scanning apparatus; and

FIG. 14 is a schematic diagram of an image-forming apparatus of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1

FIG. 1 is a cross-sectional view of the principal part along the mainscanning direction (a main scanning section) of the optical scanningapparatus in Embodiment 1 of the present invention and FIG. 2 is across-sectional view of the principal part along the sub-scanningdirection (a sub-scanning section) of FIG. 1.

In the present specification the main scanning direction (meridionaldirection) is defined along the direction into which the light isreflectively deflected (or deflected to scan) by the deflecting means,and the sub-scanning direction (sagittal direction) along the directionperpendicular to the optical axis of the scanning optical means and tothe main scanning direction.

In the figures, numeral 1 designates a light source means, which iscomprised, for example, of a semiconductor laser. Numeral 2 denotes acollimator lens (condenser lens), which converts a diverging beam (lightbeam) emitted from the light source means 1 into a nearly parallel beam.Numeral 3 represents an aperture stop, which limits passing light(amount of light). Numeral 4 indicates a cylindrical lens (anamorphiclens), which has a predetermined power only in the sub-scanningdirection and which focuses the beam having passed the aperture stop 3in an almost linear image on a deflection facet (reflective surface) 5 aof an optical deflector 5 described hereinafter, in the sub-scanningsection. Each of the elements including the collimator lens 2, theaperture stop 3, the cylindrical lens 4, and so on constitutes anelement of entrance optical means 11.

Numeral 5 denotes the optical deflector as the deflecting means, whichis comprised, for example, of a polygon mirror (rotary polygon mirror)and which is rotated at a fixed speed in the direction of arrow A in thedrawing by a driving means such as a motor or the like (notillustrated).

Numeral 6 denotes the scanning optical means having the convergingfunction and the fθ characteristics, which has first and second fθlenses (scanning lenses) 6 a, 6 b of the shape described hereinafter,which focuses the beam based on the image information, which wasreflectively deflected by the optical deflector 5, on a photosensitivedrum surface 7 as a surface to be scanned, and which has an inclinationcorrecting function by keeping the deflection facet 5 a of the opticaldeflector 5 in conjugate with the surface to be scanned 7 in thesub-scanning section. In the scanning optical means 6 the first fθ lens6 a on the side of optical deflector 5 has a negative, refractive powerin the sub-scanning direction and the second fθ lens 6 b on the side ofthe surface to be scanned 7 has a positive, refractive power in thesub-scanning direction.

Numeral 7 represents a surface of a photosensitive drum (a surface of animage carrier) as a surface to be scanned.

In the present embodiment the diverging beam emitted from thesemiconductor laser 1 is converted into a nearly parallel beam by thecollimator lens 2 and the beam (amount of light) is limited by theaperture stop 3 to enter the cylindrical lens 4. The nearly parallelbeam entering the cylindrical lens 4 emerges in the as-entering state inthe main scanning section. In the sub-scanning section the beam isconverged to be focused as an almost linear image (a linear imagelongitudinal in the main scanning direction) on the deflection facet 5 aof the optical deflector 5. Then the beam reflectively deflected by thedeflection facet 5 a of the optical deflector 5 travels through thefirst fθ lens 6 a and the second fθ lens 6 b to be focused in a spotshape on the surface of the photosensitive drum 7. The optical deflector5 is rotated in the direction of arrow A, whereby the beam opticallyscans the surface of the photosensitive drum 7 at an equal speed in thedirection of arrow B (in the main scanning direction). This causes animage to be recorded on the photosensitive drum surface 7 as a recordingmedium.

The optical layout of the scanning optical means 6 and asphericalcoefficients of the first and second fθ lenses 6 a, 6 b in the presentembodiment are presented in Table 1 and Table 2, respectively. FIG. 3and FIG. 4 are drawings to show how curvatures in the sagittal directionvary in each of surfaces of the first and second fθ lenses 6 a, 6 b,respectively, in the present embodiment.

TABLE 1 LAYOUT OF OPTICAL SCANNING APPARATUS fθ COEFFICIENT (mm/rad) fθCOEFFICIENT k 109 WAVELENGTH, REFRACTIVE INDEX WAVELENGTH USED λ (nm)780 fθ LENS 6a REFRACTIVE INDEX N1 1.5242 fθ LENS 6b REFRACTIVE INDEX N21.5242 PLACEMENT OF IMAGING OPTICAL SYSTEM (mm) REFLECTIVE SURFACE OFPOLYGON d1 10.50 MIRROR 5a - LENS 6a INCIDENCE SURFACE 6ai LENS 6aINCIDENCE SURFACE 6ai - d2 7.05 LENS 6a EXIT SURFACE 6ao LENS 6a EXITSURFACE 6ao - LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS 6b INCIDENCESURFACE 6bi - d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXIT SURFACE6bo - d5 102.45 SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm) W 214k/W k/W 0.51 SUB-SCANNING MAGNIFICATION βs 3.3

TABLE 2 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6a MERIDIONAL SHAPEfθ LENS 6b MERIDIONAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6aiSURFACE 6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHTLIGHT LIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE R−3.02877E+01 −2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00−1.20217E+00 K −6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.57451E−05 B4−1.46498E−05 −2.14482E−05 B6 −8.09230E−08  3.57693E−08 B6  1.26772E−08 2.47677E−08 B8  0.00000E+00 −1.12626E−10 B8 −1.36311E−12 −2.71180E−11B10  0.00000E+00  0.00000E+00 B10 −2.45186E−15  2.06855E−14 B12 0.00000E+00  0.00000E+00 B12  0.00000E+00 −6.92697E−18 ON THE ON THE ONTHE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE R −3.02877E+01−2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00 −1.20217E+00 K−6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.49085E−05 B4 −1.63400E−05−2.24876E−05 B6 −8.09230E−08  4.08194E−08 B6  1.64210E−08  2.67132E−08B8  0.00000E+00 −1.20672E−10 B8 −4.36204E−12 −2.94646E−11 B10 0.00000E+00  0.00000E+00 B10 −2.17220E−15  2.28464E−14 B12  0.00000E+00 0.00000E+00 B12  0.00000E+00 −8.12057E−18 fθ LENS 6a SAGITTAL SHAPE fθLENS 6b SAGITTAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6ai SURFACE6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHT LIGHTLIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE r−1.00000E+01 −2.32587E+01 r  7.18760E+01 −1.26284E+01 D2  0.00000E+00−1.48301E−03 D2 −1.19364E−03  1.44964E−03 D4  0.00000E+00 −2.46682E−06D4  1.96871E−06 −2.17689E−06 D6  0.00000E+00  4.91740E−09 D6−1.63328E−10  2.44849E−09 D8  0.00000E+00  1.13169E−11 D8 −1.09555E−13−1.26980E−12 D10  0.00000E+00 −1.90462E−15 D10  1.42201E−16  8.86595E−17D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00 ON THE ONTHE ON THE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE r−1.00000E+01 −2.32587E+01 r  7.18760E+01 −1.26284E+01 D2  0.00000E+00−6.74273E−03 D2  7.86075E−03  1.44964E−03 D4  0.00000E+00  3.13732E−05D4 −1.20370E−05 −2.17689E−06 D6  0.00000E+00 −4.91023E−08 D6 2.30753E−09  2.44849E−09 D8  0.00000E+00 −1.96138E−12 D8  1.30133E−12−1.26980E−12 D10  0.00000E+00 −4.27397E−16 D10  4.58193E−15  8.86595E−17D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00

In the present embodiment each of meridional lens shapes of the firstand second fθ lenses 6 a, 6 b is comprised of an aspherical shape thatcan be expressed as a function up to degree 12. For example, let usdefine the origin at an intersection between the optical axis and thefirst or second fθ lens 6 a, 6 b, take the X-axis along the direction ofthe optical axis, and take the Y-axis along an axis perpendicular to theoptical axis in the main scanning section. Then the shapes in themeridional direction corresponding to the main scanning direction areexpressed by the following equation.X=(Y ² /R)/[1+{1−(1+k)(Y/R)²)}^(1/2) ]+B4×Y ⁴ +B6×Y ⁶ +B8×Y ⁸ +B10×Y ¹⁰+B12×Y ¹²(where R is a radius of curvature in the meridional direction and on theoptical axis, and k, B4, B6, B8, B10, and B12 are the asphericalcoefficients).

Sagittal lines of each lens surface continuously change their radii ofcurvatures with change in coordinates on the lens surface in the mainscanning direction. The radius R_(s)* of the curvature of the sagittalline at the position where the coordinate is Y in the main scanningdirection, is expressed by the following equation.R _(s) *=R _(s)×(1+D2×Y ² +D4×Y ⁴ +D6×Y6+D8×Y ⁸ +D10×Y¹⁰)(where R_(s) is the radius of the curvature in the sagittal directionand on the optical axis, and D2, D4, D6, D8, and D10 are coefficients).

In the present embodiment the first fθ lens 6 a is a positive meniscuslens with a concave surface opposed to the polygon mirror 5 in the mainscanning section and a negative meniscus lens with a concave surfaceopposed to the polygon mirror 5 in the sub-scanning section.

The second fθ lens 6 b is a positive meniscus lens with a convex surfaceopposed to the polygon mirror 5 in the main scanning section and adouble-convex lens with a convex surface opposed to the polygon mirror 5and the other convex surface to the surface to be scanned 7 in thesub-scanning section.

In the incidence surface 6 ai of the first fθ lens 6 a, the surfaces inthe main scanning and sub-scanning directions both are symmetric in themain scanning direction with respect to the optical axis, and thesurface consists of a surface of a constant curvature in the sagittaldirection (hereinafter also referred to as “sagittal curvature”) normalto the meridional line in the main scanning section.

In the exit surface 6 ao of the first fθ lens 6 a, the surface in themain scanning direction is asymmetric with respect to the optical axis,and the surface in the sub-scanning direction consists of a sagittalasymmetric change surface in which curvatures in the sagittal directionchange on an asymmetric basis in the main scanning direction withrespect to the optical axis.

In the incidence surface 6 bi of the second fθ lens 6 b, the surface inthe main scanning direction is asymmetric with respect to the opticalaxis, and the surface in the sub-scanning direction consists of asagittal asymmetric change surface in which curvatures in the sagittaldirection change on an asymmetric basis in the main scanning directionwith respect to the optical axis.

In the exit surface 6 bo of the second fθ lens 6 b, the surface in themain scanning direction is asymmetric with respect to the optical axis,and the surface in the sub-scanning direction consists of a surface inwhich curvatures in the sagittal direction increase on a symmetric basisin the main scanning direction on either side of the optical axis.

FIG. 5 is an aberration diagram to show the curvature of field in thesub-scanning direction and ratios of sub-scanning magnifications of theoptical scanning apparatus in the present embodiment. FIG. 6 is adiagram to show the curvature of field in the sub-scanning direction andratios of sub-scanning magnifications in the present embodiment (solidlines) and a comparative example (dashed lines) wherein curvatures inthe sagittal direction on the anti-source side (i.e., on the other sidethan the side of the light source means 1 with respect to the opticalaxis of the scanning optical means 6) are equal to those on the lightsource side (i.e., on the same side as the light source means 1 withrespect to the optical axis of the scanning optical means 6) so that thecurvatures in the sagittal direction of the scanning optical means 6 inthe present embodiment are symmetric in the main scanning direction withrespect to the optical axis in all the four surfaces.

It is seen from FIG. 5 and FIG. 6 that the curvature of field in thesub-scanning direction and the asymmetry of sub-scanning magnificationsare corrected well in the present embodiment.

In the present embodiment, where the fθ coefficient of the scanningoptical means 6 is k and the effective scanning width on the surface tobe scanned 7 is W, the following condition is satisfied:k/w≦0.6.

When the lateral magnification in the sub-scanning direction of thescanning optical means 6 is β_(s), the following condition is satisfied:|β_(s)|?2.

In the present embodiment the fθ coefficient of the scanning opticalmeans 6 is set to k=109 (mm/rad), the effective scanning width on thesurface to be scanned 7 to W=214 mm, the angles of view to the wideangles of view over ±56°, and the sub-scanning magnification to|β_(s)|3.3.

In general, in the optical scanning apparatus, when the light emittedfrom the light source means is reflectively deflected at the deflectionfacet of the polygon mirror, the position of reflection varies dependingupon angles of view and deviation of the reflection position isasymmetric with respect to the optical axis of the scanning opticalmeans. This makes the image positions asymmetric in the main scanningand sub-scanning directions and also makes the sub-scanningmagnifications asymmetric. In the case wherein the angles of view arethe wide angles of view over ±47° and the sub-scanning magnifications(|β_(s)|≧2) are high as in the present embodiment, the asymmetry of thesub-scanning magnifications and the curvature of field (image positions)in the sub-scanning direction appears more prominent.

In the present embodiment the scanning optical means 6 is thusconstructed of the combination of the surfaces wherein the curvatures inthe sagittal direction change on an asymmetric basis as described above,whereby the asymmetry of the sub-scanning magnifications and thecurvature of field (image positions) in the sub-scanning direction canbe corrected well even in the case of the wide angles of view and thehigh sub-scanning magnifications. This permits the spot size in thesub-scanning direction to be kept constant at all the scanning positionsin the effective scanning area on the surface to be scanned.

In the present embodiment, as described above, the scanning opticalmeans 6 is thus constructed of the plurality of sagittal asymmetricchange surfaces and the shape of each lens is properly set, whereby thecurvature of field is corrected well in the sub-scanning direction whilethe image magnifications in the sub-scanning direction are correctedinto a constant value, so as to make the spot size uniform in thesub-scanning direction.

In the present embodiment the scanning optical means 6 was constructedof the two fθ lenses 6 a, 6 b, but the present invention is not limitedto this example; for example, the present invention can also be appliedto configurations in which the scanning optical means 6 is composed ofone fθ lens or of three or more fθ lenses, similarly as in aboveEmbodiment 1.

Embodiment 2

Described next is the multi-beam optical scanning apparatus inEmbodiment 2 of the present invention.

The present embodiment is different from above Embodiment 1 in that thelight source means 1 is comprised of a multi-beam semiconductor laserconsisting of two light-emitting regions and in that degrees of changeare different for the curvatures in the sagittal direction in thesurfaces of the first and second fθ lenses 6 a, 6 b constituting thescanning optical means 6. The other structure and optical action aresubstantially the same as in Embodiment 1, thereby achieving likeeffect.

The optical layout of the scanning optical means 6 and the asphericalcoefficients of the first and second fθ lenses 6 a, 6 b in the presentembodiment are presented in Table 3 and Table 4, respectively. FIG. 7and FIG. 8 are diagrams to show how the curvatures in the sagittaldirection change in each of the surfaces of the first and second fθlenses 6 a, 6 b, respectively, in the present embodiment.

TABLE 3 LAYOUT OF OPTICAL SCANNING APPARATUS fθ COEFFICIENT (mm/rad) fθCOEFFICIENT k 109 WAVELENGTH, REFRACTIVE INDEX WAVELENGTH USED λ (nm)780 fθ LENS 6a REFRACTIVE INDEX N1 1.5242 fθ LENS 6b REFRACTIVE INDEX N21.5242 PLACEMENT OF IMAGING OPTICAL SYSTEM (mm) REFLECTIVE SURFACE OFPOLYGON d1 10.50 MIRROR 5a - LENS 6a INCIDENCE SURFACE 6ai LENS 6aINCIDENCE SURFACE 6ai - d2 7.05 LENS 6a EXIT SURFACE 6ao LENS 6a EXITSURFACE 6ao - LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS 6b INCIDENCESURFACE 6bi - d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXIT SURFACE6bo - d5 102.45 SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm) W 214k/W k/W 0.51 SUB-SCANNING MAGNIFICATION βs 3.3

TABLE 4 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6a MERIDIONAL SHAPEfθ LENS 6b MERIDIONAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6aiSURFACE 6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHTLIGHT LIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE R−3.02877E+01 −2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00−1.20217E+00 K −6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.57451E−05 B4−1.46498E−05 −2.14482E−05 B6 −8.09230E−08  3.57693E−08 B6  1.26772E−08 2.47677E−08 B8  0.00000E+00 −1.12626E−10 B8 −1.36311E−12 −2.71180E−11B10  0.00000E+00  0.00000E+00 B10 −2.45186E−15  2.06855E−14 B12 0.00000E+00  0.00000E+00 B12  0.00000E+00 −6.92697E−18 ON THE ON THE ONTHE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE R −3.02877E+01−2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00 −1.20217E+00 K−6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.49085E−05 B4 −1.63400E−05−2.24876E−05 B6 −8.09230E−08  4.08194E−08 B6  1.64210E−08  2.67132E−08B8  0.00000E+00 −1.20672E−10 B8 −4.36204E−12 −2.94646E−11 B10 0.00000E+00  0.00000E+00 B10 −2.17220E−15  2.28464E−14 B12  0.00000E+00 0.00000E+00 B12  0.00000E+00 −8.12057E−18 fθ LENS 6a SAGITTAL SHAPE fθLENS 6b SAGITTAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6ai SURFACE6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHT LIGHTLIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE r−1.00000E+01 −2.09964E+01 r  6.48557E+01 −1.30869E+01 D2  4.28806E−03 1.94201E−03 D2 −1.36754E−03  1.31246E−03 D4  0.00000E+00 −2.44214E−06D4  2.41168E−06 −1.74690E−06 D6  0.00000E+00 −3.45544E−08 D6−5.36054E−10  1.72030E−09 D8  0.00000E+00  7.76111E−11 D8 −2.34886E−13−8.99867E−13 D10  0.00000E+00 −1.84716E−15 D10  1.12331E−16  1.13837E−16D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00 ON THE ONTHE ON THE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE r−1.00000E+01 −2.09964E+01 r  6.48557E+01 −1.30869E+01 D2  0.00000E+00−6.25001E−03 D2  9.15047E−03  1.31246E−03 D4  0.00000E+00  2.87184E−05D4 −1.10470E−05 −1.74690E−06 D6  0.00000E+00 −4.47732E−08 D6 2.23789E−09  1.72030E−09 D8  0.00000E+00 −1.98582E−12 D8  1.28175E−12−8.99867E−12 D10  0.00000E+00 −4.28401E−16 D10  4.13805E−15  1.13837E−17D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00

In the present embodiment, in the incidence surface 6 ai of the first fθlens 6 a, the surface in the sub-scanning direction consists of asagittal asymmetric change surface in which curvatures in the sagittaldirection change on an asymmetric basis in the main scanning directionwith respect to the optical axis. Further, the magnitude relation amongthe curvatures in the sagittal direction is as follows.

-   -   curvatures on the light source side>curvature on the optical        axis=curvatures on the anti-source side

Therefore, the surface is also a sagittal deformation surface in whichthe magnitude relation differs among the curvatures in the sagittaldirection at respective positions in the main scanning direction withrespect to the optical axis.

In the exit surface 6 ao of the first fθ lens 6 a, the surface in thesub-scanning direction consists of a sagittal asymmetric change surfacein which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis.

Further, the magnitude relation among the curvatures in the sagittaldirection is as follows.

-   -   curvatures on the light source side>curvature on the optical        axis>curvatures on the anti-source side.

Thus, the surface is also a sagittal deformation surface in which themagnitude relation differs among the curvatures in the sagittaldirection at respective positions in the main scanning direction withrespect to the optical axis.

In the incidence surface 6 bi of the second fθ lens 6 b, the surface inthe sub-scanning direction consists of a sagittal asymmetric changesurface in which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis and is also a sagittal deformation surface in which thecurvatures in the sagittal direction increase with distance from theoptical axis up to an inflection point at a middle point and thengradually decrease on the side of light source means 1 with respect tothe optical axis while the curvatures gradually decrease with distancefrom the optical axis on the other side than the side of light sourcemeans 1 (see FIG. 8).

In the exit surface 6 bo of the second fθ lens 6 b, the surface in thesub-scanning direction consists of a surface in which the curvatures inthe sagittal direction increase on a symmetric basis in the mainscanning direction on either side of the optical axis.

FIG. 9 is an aberration diagram to show the curvature of field in thesub-scanning direction and ratios of sub-scanning magnifications of theoptical scanning apparatus in the present embodiment.

In the present embodiment the curvatures in the sagittal direction arelargely changed in the incidence surface 6 ai and the exit surface 6 aoof the first fθ lens 6 a and the incidence surface 6 bi of the second fθlens 6 b, whereby better correction can be made for the curvature offield in the sub-scanning direction and the ratios of sub-scanningmagnifications.

Specifically, the position of the principal plane is largely moved bymaking the curvatures in the sagittal direction on the side of the lightsource means 1 in the incidence surface 6 ai and the exit surface 6 aoof the first fθ lens 6 a and the incidence surface 6 bi of the second fθlens 6 b all larger than the corresponding curvature in the sagittaldirection on the optical axis and making the curvatures in the sagittaldirection on the anti-source side in the exit surface 6 ao of the firstfθ lens 6 a and the incidence surface 6 bi of the second fθ lens 6 bboth smaller than the corresponding curvature in the sagittal directionon the optical axis, whereby correction is made to make the curvature offield in the sub-scanning direction and the sub-scanning magnificationsconstant. The present embodiment makes more accurate correction feasibleby changing the curvatures in the sagittal direction on either one sidein the main scanning direction with respect to the optical axis so as tohave the inflection point midway as in the state of change of thecurvatures in the sagittal direction on the light source means 1 side inthe incidence surface 6 bi of the second fθ lens 6 b.

This permits the present embodiment to keep the spot sizes of aplurality of beams in the sub-scanning direction constant irrespectiveof the scanning positions in the effective scanning area on the surfaceto be scanned 7 and to keep the line pitch intervals constantirrespective of the scanning positions on the surface to be scanned 7during the optical scanning of the surface to be scanned 7 with thebeams, thereby realizing the multi-beam optical scanning apparatuscapable of always obtaining good images without pitch irregularity.

Embodiment 3

Described next is the multi-beam optical scanning apparatus inEmbodiment 3 of the present invention.

The present embodiment is different from above Embodiment 2 in that allthe lens surfaces of the first and second fθ lenses 6 a, 6 bconstituting the scanning optical means 6 are formed in the concaveshape opposed to the optical deflector 5 and in that degrees of changein the curvatures in the sagittal direction are different. The otherstructure and optical action are substantially the same as in Embodiment2, thereby achieving like effect.

The optical layout of the scanning optical means 6 and the asphericalcoefficients of the first and second fθ lenses 6 a, 6 b in the presentembodiment are presented in Table 5 and Table 6, respectively. FIG. 10and FIG. 11 are diagrams to show how the curvatures in the sagittaldirection change in each of the surfaces of the first and second fθlenses 6 a, 6 b, respectively, in the present embodiment.

TABLE 5 LAYOUT OF OPTICAL SCANNING APPARATUS fθ COEFFICIENT (mm/rad) fθCOEFFICIENT k 109 WAVELENGTH, REFRACTIVE INDEX WAVELENGTH USED λ (nm)780 fθ LENS 6a REFRACTIVE INDEX N1 1.5242 fθ LENS 6b REFRACTIVE INDEX N21.5242 PLACEMENT OF IMAGING OPTICAL SYSTEM (mm) REFLECTIVE SURFACE OFPOLYGON d1 10.50 MIRROR 5a - LENS 6a INCIDENCE SURFACE 6ai LENS 6aINCIDENCE SURFACE 6ai - d2 7.05 LENS 6a EXIT SURFACE 6ao LENS 6a EXITSURFACE 6ao - LENS d3 6.45 6b INCIDENCE SURFACE 6bi LENS 6b INCIDENCESURFACE 6bi - d4 7.55 LENS 6b EXIT SURFACE 6bo LENS 6b EXIT SURFACE6bo - d5 102.45 SURFACE TO BE SCANNED 7 EFFECTIVE SCAN WIDTH (mm) W 214k/W k/W 0.51 SUB-SCANNING MAGNIFICATION βs 3.1

TABLE 6 LAYOUT OF OPTICAL SCANNING APPARATUS fθ LENS 6a MERIDIONAL SHAPEfθ LENS 6b MERIDIONAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6aiSURFACE 6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHTLIGHT LIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE R−3.02877E+01 −2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00−1.20217E+00 K −6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.57451E−05 B4−1.46498E−05 −2.14482E−05 B6 −8.09230E−08  3.57693E−08 B6  1.26772E−08 2.47677E−08 B8  0.00000E+00 −1.12626E−10 B8 −1.36311E−12 −2.71180E−11B10  0.00000E+00  0.00000E+00 B10 −2.45186E−15  2.06855E−14 B12 0.00000E+00  0.00000E+00 B12  0.00000E+00 −6.92697E−18 ON THE ON THE ONTHE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE R −3.02877E+01−2.16472E+01 R  8.14379E+01  7.96757E+01 K −2.52957E+00 −1.20217E+00 K−6.69965E+00 −1.39708E−01 B4  3.61254E−05  1.49085E−05 B4 −1.63400E−05−2.24876E−05 B6 −8.09230E−08  4.08194E−08 B6  1.64210E−08  2.67132E−08B8  0.00000E+00 −1.20672E−10 B8 −4.36204E−12 −2.94646E−11 B10 0.00000E+00  0.00000E+00 B10 −2.17220E−15  2.28464E−14 B12  0.00000E+00 0.00000E+00 B12  0.00000E+00 −8.12057E−18 fθ LENS 6a SAGITTAL SHAPE fθLENS 6b SAGITTAL SHAPE INCIDENCE EXIT INCIDENCE EXIT SURFACE 6ai SURFACE6ao SURFACE 6bi SURFACE 6bo ON THE ON THE ON THE ON THE LIGHT LIGHTLIGHT LIGHT SOURCE SIDE SOURCE SIDE SOURCE SIDE SOURCE SIDE r−1.00000E+01 −2.12739E+01 r −5.12420E+01 −1.00000E+01 D2  1.48475E−02 1.37384E−02 D2  1.35236E−02  1.50729E−03 D4  0.00000E+00 −8.27842E−07D4 −2.66781E−05 −4.37989E−06 D6  0.00000E+00 −8.53731E−11 D6−2.05461E−09  7.77917E−09 D8  0.00000E+00  4.22219E−10 D8  1.19594E−10−6.41723E−12 D10  0.00000E+00 −0.00000E−00 D10  3.72456E−14  1.95495E−15D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00 ON THE ONTHE ON THE ON THE OTHER SIDE OTHER SIDE OTHER SIDE OTHER SIDE r−1.00000E+01 −2.12739E+01 r −5.12420E+01 −1.00000E+01 D2  0.00000E+00−7.11965E−03 D2 −1.50314E−03  1.50729E−03 D4  0.00000E+00  3.95789E−05D4  3.61267E−06 −4.37989E−06 D6  0.00000E+00 −7.31415E−08 D6 9.01459E−10  7.77917E−09 D8  0.00000E+00 −4.99893E−13 D8 −8.13695E−14−6.41723E−12 D10  0.00000E+00  0.00000E+00 D10 −3.56630E−15  1.95495E−15D12  0.00000E+00  0.00000E+00 D12  0.00000E+00  0.00000E+00

In the present embodiment the first fθ lens 6 a consists of a negativemeniscus lens with a concave surface opposed to the polygon mirror 5 inthe sub-scanning section and the second fθ lens 6 b consists of apositive meniscus lens with a concave surface opposed to the polygonmirror 5 in the sub-scanning section. This structure permits thesub-scanning magnification to be decreased to a small value even in thesame positional layout.

In the present embodiment the sub-scanning magnification |β_(s)|=3.1.

In the incidence surface 6 ai of the first fθ lens 6 a, the surface inthe sub-scanning direction consists of a sagittal asymmetric changesurface in which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis.

Further, the magnitude relation among the curvatures in the sagittaldirection is as follows.

-   -   curvatures on the light source side>curvature on the optical        axis=curvatures on the anti-source side

Therefore, the surface is also a sagittal deformation surface in whichthe magnitude relation differs among the curvatures in the sagittaldirection at the respective positions in the main scanning directionwith respect to the optical axis.

In the exit surface 6 ao of the first fθ lens 6 a, the surface in thesub-scanning direction consists of a sagittal asymmetric change surfacein which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis.

Further, the magnitude relation among the curvatures in the sagittaldirection is as follows.

-   -   curvatures on the light source side>curvature on the optical        axis>curvatures on the anti-source side

Thus, the surface is also a sagittal deformation surface in which themagnitude relation differs among the curvatures in the sagittaldirection at the respective positions in the main scanning directionwith respect to the optical axis.

In the incidence surface 6 bi of the second fθ lens 6 b, the surface inthe sub-scanning direction consists of a sagittal asymmetric changesurface in which the curvatures in the sagittal direction change on anasymmetric basis in the main scanning direction with respect to theoptical axis and is also a sagittal deformation surface in which thecurvatures in the sagittal direction gradually increase on the side oflight source means 1 with respect to the optical axis but the curvaturesin the sagittal direction first decrease to an inflection point midwayand then gradually increase thereafter on the anti-source side.

In the exit surface 6 bo of the second fθ lens 6 b, the surface in thesub-scanning direction consists of a surface in which the curvatures inthe sagittal direction increase on a symmetric basis in the mainscanning direction on either side of the optical axis.

FIG. 12 is an aberration diagram to show the curvature of field in thesub-scanning direction and ratios of sub-scanning magnifications of theoptical scanning apparatus in the present embodiment.

In the present embodiment, similarly as in above Embodiment 2, aplurality of surfaces are used to effect such bending as to make thechange in the curvatures in the sagittal direction inclined in the samedirection, whereby the asymmetry of sub-scanning magnifications and thecurvature of field in the sub-scanning direction can be corrected wellsimultaneously even in the case of the wide angles of view and the highsub-scanning magnifications.

It is needless to mention that the configurations in above Embodiments2, 3 can also be applied to the optical scanning apparatus using asingle optical beam.

FIG. 14 is a cross-sectional view of the principal part along thesub-scanning direction to show an embodiment of the image-formingapparatus of the present invention. In FIG. 14, numeral 104 designatesthe image-forming apparatus. This image-forming apparatus 104 acceptsinput of code data Dc from an external device 117 such as a personalcomputer or the like. This code data Dc is converted into image data(dot data) Di by a printer controller 111 in the apparatus. This imagedata Di is supplied to an optical scanning unit 100 having the structureas described in either of Embodiments 1 to 3. This optical scanning unit100 outputs an optical beam 103 modulated according to the image data Diand this light beam 103 scans a photosensitive surface of photosensitivedrum 101 in the main scanning direction.

The photosensitive drum 101 as an electrostatic latent image carrier(photosensitive body) is rotated clockwise by a motor 115. With therotation thereof, the photosensitive surface of the photosensitive drum101 moves in the sub-scanning direction perpendicular to the mainscanning direction, relative to the light beam 103. Above thephotosensitive drum 101, a charging roller 102 for uniformly chargingthe surface of the photosensitive drum 101 is disposed so as to contactthe surface. Then the surface of the photosensitive drum 101 charged bythe charging roller 102 is exposed to the light beam 103 under scanningby the optical scanning unit 100.

As described previously, the light beam 103 is modulated based on theimage data Di and an electrostatic latent image is formed on the surfaceof the photosensitive drum 101 under irradiation with this light beam103. This electrostatic latent image is developed into a toner image bya developing unit 107 disposed so as to contact the photosensitive drum101 downstream in the rotating direction of the photosensitive drum 101from the irradiation position of the light beam 101.

The toner image developed by the developing unit 107 is transferred ontoa sheet 112 being a transfer medium, by a transfer roller 108 opposed tothe photosensitive drum 101 below the photosensitive drum 101. Sheets112 are stored in a sheet cassette 109 in front of (i.e., on the rightside in FIG. 14) of the photosensitive drum 101, but sheet feed can alsobe implemented by hand feeding. A sheet feed roller 110 is disposed atan end of the sheet cassette 109 and feeds each sheet 112 in the sheetcassette 109 into the conveyance path.

The sheet 112 onto which the toner image unfixed was transferred asdescribed above, is further transferred to a fixing unit located behindthe photosensitive drum 101 (i.e., on the left side in FIG. 14). Thefixing unit is composed of a fixing roller 113 having a fixing heater(not illustrated) inside and a pressing roller 114 disposed in presscontact with the fixing roller 113 and heats while pressing the sheet112 thus conveyed from the transfer part, in the nip part between thefixing roller 113 and the pressing roller 114 to fix the unfixed tonerimage on the sheet 112. Sheet discharge rollers 116 are disposed furtherbehind the fixing roller 113 to discharge the fixed sheet 112 to theoutside of the image-forming apparatus.

Although not illustrated in FIG. 14, the print controller 111 alsoperforms control of each section in the image-forming apparatus,including the motor 115, and control of the polygon motor etc. in theoptical scanning unit described above, in addition to the conversion ofdata described above.

Further, the present invention may also be applied to configurations inwhich sagittal asymmetric change surfaces are laid on four or moresurfaces of lenses constituting the fθ lenses.

In Embodiments 2, 3 the number of the light-emitting regions of thelight source means was two, but the present invention can also beapplied to a plurality of light-emitting regions not less than three.

According to the present invention, the optical scanning means isconstructed of a plurality of sagittal asymmetric change surfaces andthe shape of each lens is properly set in the optical scanning apparatusin which light is incident at angles in the main scanning direction tothe deflecting means as described previously, whereby good correctioncan be made for the asymmetry of the sub-scanning magnifications and thecurvature of field in the sub-scanning direction occurring in the casewherein the deflecting means is the rotary polygon mirror. This canaccomplish the compact, high-definition, optical scanning apparatuscapable of keeping the spot size uniform in the sub-scanning directionthroughout the entire, effective scanning area on the surface to bescanned.

According to the present invention, the scanning optical means isconstructed of a plurality of sagittal asymmetric change surfaces andthe shape of each lens is properly set in the multi-beam opticalscanning apparatus as described above, whereby the invention canaccomplish the compact, high-definition, multi-beam optical scanningapparatus without pitch irregularity capable of keeping the line pitchintervals in the sub-scanning direction constant throughout the entire,effective scanning area.

1. An optical scanning apparatus comprising: a light source; deflectingmeans; entrance optical means for guiding light emitted from the lightsource to the deflecting means; and scanning optical means for formingan image of the light reflectively deflected by the deflecting means, ona surface to be scanned; wherein said scanning optical meansasymmetrically changes curvatures in a sagittal direction at respectivepositions in a meridional direction; wherein the curvatures in thesagittal direction at respective positions in the meridional directionfacing in one off-axis direction across an optical axis comprise aplurality of sagittal deformation surfaces of which magnitude relationis larger than that in curvatures in the sagittal direction atrespective positions in the meridional direction facing in anotheroff-axis direction across the optical axis; and wherein the sagittaldeformation surfaces comprise two or more surfaces in which thecurvatures in the sagittal direction at the respective positions in themeridional direction increase or decrease on a same side.
 2. An opticalscanning apparatus according to claim 1, wherein the sagittaldeformation surfaces at respective positions of the curvatures in themeridional direction on a light source side are larger than those at therespective positions of the curvatures in the meridional direction on ananti-light source side.
 3. The optical scanning apparatus according toclaim 1, wherein the following condition is satisfied:k/W≦0.6, where k is an fθ coefficient of said scanning optical means,and W is an effective scanning width of said surface to be scanned. 4.The optical scanning apparatus according to claim 1, wherein thefollowing condition is satisfied:|β_(s)|≧2, where β_(s) is a lateral magnification in the sub-scanningdirection of said scanning optical means.
 5. An optical scanningapparatus according to claim 1, wherein two or more of the sagittaldeformation surfaces asymmetrically change curvature in the sagittaldirection at respective positions in the meridional direction so as tokeep a sub-scanning magnification constant.
 6. An optical scanningapparatus comprising: a light source; deflecting means; entrance opticalmeans for guiding light emitted from the light source to the deflectingmeans; and scanning optical means for forming an image of the lightreflectively deflected by the deflecting means, on a surface to bescanned; wherein the scanning optical means comprises a plurality ofsagittal asymmetric change surfaces in which curvatures in the sagittaldirection change on an asymmetric basis in the meridional direction withrespect to the optical axis of the scanning optical means; and whereinsaid scanning optical means comprises a plurality of fθ lenses, an fθlens located closest to the deflecting means among said plurality of fθlenses has a negative refractive power in the sagittal direction, and anfθ lens located closest to the surface to be scanned, among saidpluarlity of fθ lenses, has a positive refractive power in the sagittaldirection.
 7. The optical scanning apparatus according to claim 6,wherein all lens surfaces of said plurality of fθ lenses are formed in aconcave shape opposed to said deflecting means.
 8. An image-formingapparatus comprising: the scanning optical apparatus as set forth in anyone of claims 1 and 6; a photosensitive body located at the surface tobe scanned; a developing unit for developing an electrostatic, latentimage formed on said photosensitive body with the light under scan bysaid scanning optical apparatus, into a toner image; a transfer unit fortransferring the developed toner image onto a transfer medium; and afixing unit for fixing the transferred toner image on the transfermedium.
 9. An image-forming apparatus comprising the scanning opticalapparatus as set forth in any one of claims 1 and 6; and a printercontroller for converting code data supplied from an external device,into an image signal and supplying the image signal to said scanningoptical apparatus.